Question
A rocket is fired vertically with a speed of v km/s from the surface of the earth. Find the maximum height attained by the rocket before it returns to the earth. Take GM =gR2 at the surface of the earth.
Solution
Let a rocket of mass m be projected from the surface of the earth with velocity v less than escape velocity of satellite.
Let h be the maximum height attained by satellite before it returns to the surface of the earth.
Using law of conservation of the energy,
Total energy at surface of earth = total energy at height h
i.e.
∴
'h' is the maximum height attained by the rocket before it returns to the Earth.
Let h be the maximum height attained by satellite before it returns to the surface of the earth.
Using law of conservation of the energy,
Total energy at surface of earth = total energy at height h
i.e.
∴
'h' is the maximum height attained by the rocket before it returns to the Earth.
